Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and sauté until softened, about 5 minutes.
Stir in the minced garlic, diced carrot, and celery; cook until the vegetables start to soften, about 3-4 minutes.
Add the sliced kielbasa sausage to the pot and cook until browned, about 5 minutes.
Pour in the chicken or vegetable broth, and add the drained beans, dried thyme, and dried oregano. Stir well to combine.
Bring the mixture to a simmer, then reduce the heat to low and cook for 15 minutes, allowing the flavors to meld.
For a creamier texture, use an immersion blender to blend a portion of the soup, or transfer a cup or two to a regular blender, blend, and return to the pot.
Stir in the heavy cream, and season with salt and pepper to taste. Heat through for another 5 minutes.
Serve hot, garnished with fresh parsley if desired.